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A method involving the combination of solution processing and high-temperature synthesis was developed to fabricate xBiFeO3/(1-x)BaTiO3 core-shell nanostructure with x from 0.6 to 1. It was found that both saturation magnetisation and dielectric properties of xBiFeO3/(1-x)BaTiO3 nanostructures increase with the content of BaTiO3 decreasing. Interestingly, the improved magnetic and dielectric properties were found in 0.8BFO/0.2BTO nanostructure. The authors attribute the enhancement of magnetic and dielectric properties to the core-shell nanostructure and morphotropic phase boundary in a BiFeO3/BaTiO3 nanostructure.